Since April 19th I have seen a few other people post about this issue of the park and home buttons in the MacOS version of Sky Safari not performing the Home, Park3 and Park 4 to the correct location. Since that time SkySafari 6 Plus for Mac OS has been updated to 6.8.2. It has taken a couple of weeks to test the new version with my MacBook Pro but today after testing it I found that clicking on Park3 does no longer moves the telescope. Park 4 does go to the Park 3 position, Home telescope goes to park 4 position. This testing was done using my MacBook Pro with High Sierra, and my Mac Mini with Big Sur Mac OS 11.3.
I also ran the SkySafari 6 Plus iPad app on my M1 Mac Mini which works perfectly, just like it does on my iPad Pro.
Please let the people that are working with you on Sky Safari that it is still in need of being fixed on Mac OS 10.13 and Mac OS 11.3.1.